Collider searches of a new scalar that mixes with the Higgs combined with measurements of Higgs properties provide constraints on the mixing angle [1]}, [2]}. In our study, the mass of the second Higgs is above the electroweak scale, and hence, we take the bound \(\sin \theta _B \le 0.3\) . In Fig. REF  we present the predictions for the spin-independent cross-section for different values of the gauge coupling. In order to select the points we proceed as follows. First, we select those points that give the measured relic abundance of \(\Omega _{\rm {DM}} h^2 = 0.1197 \pm 0.0022\) . Then, we remove those points that do not satisfy LHC and/or perturbativity bounds. This is the reason behind the discontinuities in the points shown.
